Question

"A firm is considering purchasing a computer system.
-Cost of system is $198,000. The firm will pay for the computer system in year 0.
-Project life: 5 years
-Salvage value in year 0 (constant) dollars: $10,000
-Depreciation method: five-years MACRS
-Marginal income-tax rate = 40% (remains constant over time)
-Annual revenue = $147,000 (year-0 constant dollars)
-Annual expenses (not including depreciation) = $88,000 (year-0 constant dollars)
-The general inflation rate is 4.9% during the project period (which will affect all revenues, expenses, and the salvage value but not depreciation).
-The firm borrows the entire $198,000 at 14.9% interest to be repaid in 2 annual payments. The debt interest paid and the principal payment SHOULD NOT be changed by the inflation rate. Lending agencies set the interest rate of borrowing to account for the inflation rate.
Calculate the effects of borrowing and include the debt interest paid and the principal repayment into the income statement and cash flow statement. Determine the INFLATION-FREE IRR' of the computer system. Enter your answer as a percentage between 0 and 100."

Answer 1

Cost of the Computer:- $198000 (Initial Cash Outflow) (C_o)

As the fund is taken in the form of a loan, therefore, we need to calculate Equal Yearly Installments given the rate of interest on the loan is 14.9%

Installment for the year is given by the formula= P*R*(1+R)^^N/(1+R)^^N-1; where P is the principal amount, N is the number of years and N the annual rate

Therefore Cash outflows of 1st and 2nd year will be=198000*(.149)*(1+.149)^²/(1.49)^²-1=$121,637.88

Salvage Value at 0 years:- $10000 (Present value of Terminal Cash Inflow)(C₅) as the project will be salvaged after it has completed 5 years

Tax Rate :- 40% (T)

Inflation Rate:- 4.9%(I)

MACRS Depreciation can be calculated as: 200% divided by the number of years of the project. Therefore

MACRS Depreciation Rate = %

Profits of the year can be calculated as Annual Revenue-Annual Expenses- Depreciation

Table for Depreciation can be calculated as

Year	Book Value	Rate of Depreciation	MACRS Rate	Depreciation through Straight Line method	Charged Depreciation
1	198000	40%	79200	39600	79200
2	118800	40%	47520	29700	47520
3	71280	40%	28512	23760	28512
4	42768	40%	17107.2	21384	21384
5	21384	40%	8553.6	21384	21384

Now we need to calculate the Profits

P1=$(147000-88000--79200)-$121637.88(Loan Repayment for the first Year)=-141837.88

P2=$(147000-88000-47520)=11480

P3=$(147000-88000-28512)=30488

P4=$(147000-88000-21384)=37616

P5=$(147000-88000-21384)=37616

Post Tax Profit=

PT1=-$141837.88

PT2=$(11480(1-T))=6888

PT3=$(30488(1-T))=18292.8

PT4=$(37616(1-T))=22569.6

PT5=$(37616(1-T))=22569.6

As we know that Depreciation is a non-cash expense, therefore, to calculate revenues Depreciation will be added back

R1=-141837.88+79200=$-63637.9

R2=6888+47520=54408

R3=18292.8+28512=46804.8

R4=22569.6+21384=43953.6

R5=22569.6+21384=43953.6

Once Revenues are calculated now e have to discount the inflation rate for cash inflows

C1=-62637.9(1/1+0.049)^1=-59712

C2=54408(1/1+0.049)^2=49443

Similarly C3=40547, C4=36298, C5=34603+10,000(1/!.049)^5(Salvage Value)=42475

C0=Initial Payment for the loan being 121637.88

Putting these values in Excel formula IRR will be

2%

Formula = IRR(C0:C5, 5)

Answer will be 2%